Question

Eccentricity of ellipse (x²)/(a²)+(y²)/(b²)=1 if it passes through points (9,5) and (12,4) is:

• A. \(\sqrt{\dfrac{3}{4}}\)
• B. \(\sqrt{\dfrac{4}{5}}\)
• C. \(\sqrt{\dfrac{5}{6}}\)
• D. √((6)/(7))

Hint:

For ellipse, e=√(1-(b²)/(a²)).

Answer 1

The Correct Option is C

Step 1: Substitute (9,5): (81)/(a²)+(25)/(b²)=1 (1)
Step 2: Substitute (12,4): (144)/(a²)+(16)/(b²)=1 (2)
Step 3: Solving (1) and (2) gives: a²=150, b²=30
Step 4: Eccentricity: e=√(1-(b²)/(a²))=√(1-(30)/(150))=√((5)/(6))